• Corpus ID: 15997221


  author={Philippe and Jacquety and Wojciech and SzpankowskizINRIA},
In combinatorics and analysis of algorithms often a Poisson version of a problem (called Poisson model or poissonization) is easier to solve than the original one, which is known as the Bernoulli model. Poissonization is a technique that replaces the original input by a Poisson process. More precisely, an analytical Poisson transform maps a sequence (e.g., characterizing the Bernoulli model) into a generating function of a complex variable. However, after poissonization one must depoissonize in… 

The Diagonal Poisson Transform and its application to the analysis of a hashing scheme

It is shown that the Robin Hood heuristic achieves minimum variance over all linear probing algorithms up to lower-order terms, and an accurate analysis of this algorithm is made by introducing a new transform which is called the Diagonal Poisson Transform as it resembles the Poisson transform.

On the distribution for the duration of a randomized leader election algorithm

We investigate the duration of an elimination process for identifying a loser by coin tossing, or, equivalently, the height of a random incomplete trie. Applications of the prOcess include the

Analysis of a splitting process arising in probabilistic counting and other related algorithms

An analytical method of analyzing a class of "splitting algorilhms" that include probabilistic counting, selecting the leader, estimating the number of questions necessary to identify distinct objects, searching algorithms based on digital tries, approximate counting, and so forth is presented.

Asymptotic Behavior of the Lempel-Ziv Parsing Scheme and Digital Search Trees

Ultimate Characterizations of the Burst Response of an Interval Searching Algorithm: A Study of a Functional Equation

The interval searching algorithm for broadcast communications of Gallager and Tsybakov and Mikhailov is analyzed. Ultimate characterizations of the burst response of the algorithm, that is, when the

Limiting Distribution for the Depth in Patricia Tries

This paper shows that the depth in the asymmetric case (i.e., symbols from the alphabet do not occur with the same probability) is asymptotically normally distributed.

Handbook of Combinatorics

Part 1 Structures: graphs - basic graph theory - paths and circuits, J.A. Bondy, connectivity and network flows, A. Frank, matchings and extensions, W.R. Pulleyblank, colouring, stable sets and

Generalized Digital Trees and Their Difference-Differential Equations

A tree partitioning process in which n elements are split into b at the root of a tree, the rest going recursively into two subtrees with a binomial probability distribution is considered, extending some familiar tree data structures of computer science like the digital trie and the digital search tree.